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String Theory Prior to the First Superstring Revolution
Early History S-Matrix Theory
Regge Trajectory
Bosonic String Theory Worldsheet
String
Bosonic String Theory
String Perturbation Theory
Tachyon Condensation
Supersymmetric Revolution Supersymmetry
RNS Formalism
GS Formalism
BPS
Superstring Revolutions
First Superstring Revolution GSO Projection
Type II String Theory
Type IIB String Theory
Type IIA String Theory
Type I String Theory
Type H String Theory
Type HO String Theory
Type HE String Theory
Second Superstring Revolution T-Duality
D-Brane
S-Duality
Horava-Witten String Theory
M-Theory
Holographic Principle
N=4 Super-Yang-Mills Theory
BFSS Matrix Theory
Matrix String Theory
(2,0) Theory
Twistor String Theory
F-Theory
String Field Theory
Pure Spinor Formalism
After the Revolutions
Phenomenology String Theory Landscape
Minimal Supersymmetric Standard Model
String Phenomenology

A D-Brane is a strongly coupled $p$-dimensional object that appears in String Theory, whose existence is required by T-Duality and is motivated by Ramond-Ramond Charges.

## From Ramond-Ramond Charges Edit this section

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The worldsheet of a string can couple to a Neveu-Schwarz B-field: $q\int_{}^{} {{{h^{ab}}}\frac{{\partial {X^\mu }}}{{\partial {\xi ^a}}}\frac{{\partial {X^\nu }}}{{\partial {\xi ^b}}}B_{\mu \nu }\sqrt { - \det {h_{ab}}} {{\text{d}}^2}\xi }$ Now, the $q$ is the EM-charge.

The worldsheet of a string can couple to graviton field (spacetime metric):

$m\int_{}^{} {{{h^{ab}}}\frac{{\partial {X^\mu }}}{{\partial {\xi ^a}}}\frac{{\partial {X^\nu }}}{{\partial {\xi ^b}}}g_{\mu \nu }\sqrt { - \det {h_{ab}}} {{\text{d}}^2}\xi }$

You can change the "$m$" to any way you like, in terms of the tension/Regge Slope parameter/string length etc.

For a dilaton field,

${q }\ell _P^2\int_{}^{} {\Phi R\sqrt { - \det {h_{\alpha \beta }}} {\text{ }}{{\text{d}}^2}\xi }$ Forget the conformal invariance for the time being. But what about Ramond-Ramond potentials? All is fine with the Ramond-Ramond Fields, but the Ramond-Ramond Potentials $C_k$ are associated with the Ramond-Ramond field $A_{k+1}$ and it is intuitive (and quite clear) that they can't couple similarly to the worldsheet. But it can for a worldhhypervolume, as long as the world-hypervolume is not 2-dimensional. It would then be given by:

${q_{{\text{RR}}}}\int_{}^{} {C_{{\mu _1}...{\mu _p}}^{p + 1}\frac{{\partial {x^{{\mu _1}}}}}{{\partial {\xi ^{{a_1}}}}}...\frac{{\partial {x^{{\mu _p}}}}}{{\partial {\xi ^{{a_p}}}}}{h^{{a_0}...{a_p}}}\sqrt { - \det {h^{{a_0}...{a_p}}}} {{\text{d}}^{p + 1}}\xi }$

Note the similarity to the other couplings. Of course, this does not really neccessitate the existence of D-Branes though.

## From T-Duality Edit this section

Considering T-Duality on open strings immediately realises that open strings with Newmann boundary conditions ("Free" strings) are mapped to those with Dirchilet boundary conditions ("Bound" strings). These "bound" strings must be attached to D-branes. Therefore, strings with Newmann boundary conditions in a String Theory would have Dirchilet boundary conditions in the T-dual theory.

Therefore, this requires the existence of D-Branes.

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